Certainly I do consider myself a member of my parish, which is a tiny mission parish of the Greek Orthodox Archdiocese in the USA. I am a somewhat limitedly active parishioner, because I am very introvert by nature, and I dislike the most common form of parish life, which is a general mingling after service, usually at lunch, when everyone chitchats with everyone. That's not my thing - I usually get uncomfortable within minutes and lose the sense that I am involved. Yet, I love to talk to my parishioners one on one, and I love to use e-mail or Facebook for this purpose. Several of my co-parishioners are my FB friends, and we "talk" daily.
However, I am not sure how would I view this matter if I lived in Ukraine. Here, in the USA, my Orthodox parish is a typical American community. Even though it belongs to GOA, it is not distinctively ethnically Greek: we have "pure" 100% ethnic Greeks, and half-Greeks (children of mixed marriages), and nonGreeks like my wife and myself. Our parish priest, though he, a graduate of the Holy Cross Greek Orthodox seminary in Brookline, MA, speaks Greek better than our young Greek parishioners, is ethnically non-Greek (actually Irish, with some Czech blood). The language used at our parish minglings is almost exclusively English. A few older parishioners sometimes sit in a corner in pairs and talk to each other in Greek, but that does not happen very often - usually even older 100% ethnic Greeks speak English when they are in a public place; and it certainly has no impact on our parish life. And there is absolutely no politics in any of our parish conversations, discussions, planning etc. None. We are completely apolitical. There is simply no need to mix politics with parish life here in the US.
Now, should I live in today's Ukraine, I assume things would be different. If I joined a canonical UOC parish, odds are, the politics, which would almost certainly be there, would definitely bother me. I would not like the obstinate desire of parishioners to communicate exclusively in Russian. Even more so, I would abhore any talk about the "common Fatherland." These things would perhaps bother me so much that I would not last in that parish; I would, sooner or later, be pushed out of it like a champaigne cork. But what if I perceived that partaking in the Eucharist in THAT kind of a parish were my only option? That's the toughest question of all...
So I don't know. Having no experience of belonging to any parish in today's Ukraine, it's hard to project.